The Orderings of Bicyclic Graphs and Connected Graphs by Algebraic Connectivity
نویسندگان
چکیده
The algebraic connectivity of a graph G is the second smallest eigenvalue of its Laplacian matrix. Let Bn be the set of all bicyclic graphs of order n. In this paper, we determine the last four bicyclic graphs (according to their smallest algebraic connectivities) among all graphs in Bn when n > 13. This result, together with our previous results on trees and unicyclic graphs, can be used to further determine the last sixteen graphs among all connected graphs of order n. This extends the results of Shao et al. [The ordering of trees and connected graphs by their algebraic connectivity, Linear Algebra Appl. 428 (2008) 1421-1438]. ∗Supported by the National Science Foundation of China (No.10871204); the Fundamental Research Funds for the Central Universities (No.09CX04003A); FRG, Hong Kong Baptist University. the electronic journal of combinatorics 17 (2010), #R162 1
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 17 شماره
صفحات -
تاریخ انتشار 2010